Math Problem Statement
Solution
The question in the image is asking:
"Чему равен определитель от произведения матриц?"
This translates to:
"What is the determinant of the product of matrices equal to?"
The answer choices are:
- Сумме определителей (Sum of determinants)
- Частному определителей (Quotient of determinants)
- Произведению определителей (Product of determinants)
Correct Answer:
The determinant of the product of matrices is equal to the product of their determinants.
So, the correct answer is:
"Произведению определителей" (Product of determinants).
Let me know if you'd like a detailed explanation or have any other questions.
Here are some related questions:
- What is the formula for the determinant of the inverse of a matrix?
- How does the determinant help in solving systems of linear equations?
- What happens to the determinant if a matrix is transposed?
- What is the determinant of a diagonal matrix?
- How can determinants be used to check matrix invertibility?
Tip: The determinant is a useful property to assess whether a matrix is invertible or singular (det = 0 means singular).
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Math Problem Analysis
Mathematical Concepts
Linear Algebra
Determinants
Matrices
Formulas
det(AB) = det(A) * det(B)
Theorems
Determinant of matrix product theorem
Suitable Grade Level
Undergraduate (Linear Algebra)
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